Make sure you’re on Slide 5: Changing the Scale (Linear) of Fitting Wealth-v-Health and Exploring Logarithmic Models.

  • Both the x- and y-axis are labeled with a sequence of numbers (e.g. 0, 2, 4, 6 …​).

1 What kind of growth do the sequences on these axes show? (circle one) Linear Quadratic Exponential Logarithmic

2 The function f is Linear, Quadratic, Exponential, or Logarithmic, and its slope is . Which two points are plotted on f?

Faking a Change in Slope

  • Click on the wrench button () in the top-right corner of the Desmos graph to open the "Graph Settings" window.

  • Change the scale of the y-axis so that - 2 ≤ y ≤ 2, making sure you can see both labeled points

3 What kind of growth does the sequence of numbers on the y-axis show now? Linear Quadratic Exponential Logarithmic

4 Did our two points on the line change? Did the slope of f change? . How did the graph change?

5 What is going on here?

6 Without changing the y-axis, change the x-axis to put the line roughly back where it was. What scale did you use? ≤ x ≤

Faking a Change to Logarithmic

  • Open the "Graph Settings" window, and expand the "More Options" section by clicking the triangle ().

  • Change the y-axis scale from Linear to Logarithmic. (The y-axis labels should change to something like 0.1, 1, 10, 100…​)

  • Drag the graph to make sure you can see both labeled points

7 What kind of growth does the sequence of numbers on the y-axis show now? Linear Quadratic Exponential Logarithmic

8 Did our two points on the line change? Did the slope of f change? . How did the graph change?

9 What is going on here?

Faking a Change to Exponential

  • Change the y-axis scale back to Linear, and the x-axis scale to Logarithmic.

  • Drag the graph to make sure you can see both labeled points

10 What kind of growth does the sequence of numbers on the x-axis show now? Linear Quadratic Exponential Logarithmic

11 Did our two points on the line change? . Did the slope of f change? . How did the graph change?

12 What is going on here?

★ Make a prediction: What do you think will happen if both axes are switched to Logarithmic?

13 Change both scales to Logarithmic. Was your prediction accurate? . What happened, and why?

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). CCbadge Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.